Geometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included.

Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem.

This monograph will be of interest to students and practitioners in the field of mathematics.

Preface

Acknowledgments


List of Publications


I. Graphs and Designs


Equilateral Point Sets in Elliptic Geometry


Strongly Regular Graphs of L2-Type and of Triangular Type


Strongly Regular Graphs with (- 1, 1,0) Adjacency Matrix Having Eigenvalue 3


Strongly Regular Graphs Derived from Combinatorial Designs


A Strongly Regular Graph Derived from the Perfect Ternary Golay Code


Spherical Codes and Designs


Graphs Related to Exceptional Root Systems


Strongly Regular Graphs Having Strongly Regular Subconstituents


II. Lines with Few Angles


Equiangular Lines


A Survey of Two-Graphs


The Regular Two-Graph on 276 Vertices


Bounds for Systems of Lines, and Jacobi Polynomials


Line Graphs, Root Systems, and Elliptic Geometry


Two-Graphs, a Second Survey


III. Matrices and Forms


Orthogonal Matrices with Zero Diagonal


Quasiregular Two-Distance Sets


A Skew Hadamard Matrix of Order 36


Symmetric Hadamard Matrices of Order 36


Quadratic Forms over GF(2)


On Two-Graphs and Shult's Characterization of Symplectic and Orthogonal Geometries Over GF(2)


The Krein Condition, Spherical Designs, Norton Algebras and Permutation Groups


IV. Non-Euclidean Geometry


The Congruence Order of the Elliptic Plane


Equi-Isoclinic Subspaces of Euclidean Spaces


Metric Problems in Elliptic Geometry


The Football


Discrete Hyperbolic Geometry


Few Distance Sets in Rp,q


Remark on Wielandt's Visibility Theorem


Complete List of Permissions